polar/cartesian comparison

Manipulate[
 GraphicsColumn[{PolarPlot[1 Sin[t] + k, {t, 0, 2 Pi},
    PlotRange -> {{-3, 3}, {-3, 3}},
    Epilog -> {Red, PointSize -> Large,
      Point[{(1 Sin[theta] + k) Cos[theta],
        (1 Sin[theta] + k) Sin[theta]}]}],
   Plot[1 Sin[t] + k, {t, 0, 2 Pi},
    PlotRange -> {-2, 2},
    Epilog -> {Red, PointSize -> Large,
      Point[{theta, 1 Sin[theta] + k}]}]},
  ImageSize -> 400],
 {{k, 0}, -1, 1}, {theta, 0, 2 Pi}]